Related papers: Projected Richardson varieties and affine Schubert…
In this paper, we construct good toroidal and minimal compactifications in the sense of Lan-Stroh for integral models of abelian-type Shimura varieties. We start with finding suitable types of cusp labels and cone decompositions which are…
We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. This generalizes the classical…
We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.
The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions called k-double Schur functions and affine double Schur…
Tangent spaces to Schubert varieties of type A were characterized by Lakshmibai and Seshadri. This result was extended to the other classical types by Lakshmibai. We give a uniform characterization of tangent spaces to Schubert varieties in…
The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal torus of G are smooth irreducible locally…
Forgetting a subspace from a partial flag yields another partial flag composed of fewer subspaces. This induces a forgetful map $\pi : X \to X'$ between the corresponding flag varieties. We prove here that, for a degree large enough, the…
We introduce the notion of a cominuscule point in a Schubert variety in a generalized flag variety for a semisimple group. We derive formulas expressing the Hilbert series and multiplicity of a Schubert variety at a cominuscule point in…
Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on…
We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…
We show a canonical injective morphism from the quantum cohomology ring QH(G/P) to the associated graded algebra of QH(G/B), which is with respect to a nice filtration on QH(G/B) introduced by Leung and the author. This tells us the…
Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized…
We consider the loci of invertible linear maps $f : \mathbb{C}^n \to {(\mathbb{C}^n)}^*$ together with pairs of flags $(E_\bullet, F_\bullet)$ in $\mathbb{C}^n$ such that the various restrictions $f : F_j \to E_i^*$ have specified ranks.…
We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all…
We give a conjectural formula for sheaves supported on (irreducible) conormal varieties inside the cotangent bundle of the Grassmannian, such that their equivariant $K$-class is given by the partition function of an integrable loop model,…
This paper investigates the geometry of regular Hessenberg varieties associated with the minimal indecomposable Hessenberg space in the flag variety of a complex reductive group. These varieties form a flat family of irreducible…
The paper computes the Witt-sheaf cohomology rings of partial flag varieties in type A in terms of the Pontryagin classes of the subquotient bundles. The proof is based on a Leray-Hirsch-type theorem for Witt-sheaf cohomology for the…
In these notes, we survey the homology of the loop group Omega(K) of a compact group K, also known as the affine Grassmannian of a complex loop group. Using the Bott picture of H_*(Omega(K)), the homology algebra or Pontryagin ring, we…
Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the…
We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a ``$q=0$'' version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of…